Equilibrium constant second order reactions

In 75 % aqueous acetic acid, the bromination of fluorene at 25 °C obeys second-order kinetics in the presence of bromide ion and higher orders in its absence287, with Ea (17.85-44.85 °C) = 17.4, log A = 10.5 and AS = —12.4 however, these values were not corrected for the bromine-tribromide ion equilibrium, the constant for which is not known in this medium, and so they are not directly comparable with the proceeding values. In the absence of bromide ion the order with respect to bromine was 2.7-2.0, being lowest when [Br2]initial was least. Second- and third-order rate coefficients were determined for reaction in 90 and 75 wt. % aqueous acetic acid as 0.0026 and 1.61 (k3/k2 = 619), 0.115 and 12.2 (k3/k2 = 106) respectively, confirming the earlier observation that the second-order reaction becomes more important as the water content is increased. A value of 7.25 x 106 was determined for f3 6 (i.e. the 2 position of fluorene). 

The role of biocatalysis in two-phase systems has many parallels with the subject we have covered under extractive reactions. It appears that a two-phase system was originally considered for transformations of water insoluble substances like steroids. Now, a series of treatises are available which teach us that the maximum value of the apparent equilibrium constant for a second-order reaction in a two-phase system can exceed the equilibrium... 

If the profile of the observed or the intrinsic rate constant plotted against pH resembles the profile for an acid-base titration curve, this strongly suggests that one of the reactants is involved in an acid-base equilibrium in that pH range. Such behavior is ftiirly common and is illustrated by the second-order reaction between the Co(II)-trien complex and O2 (Fig. 1.12). The limiting rate constants at the higher and low acidities correspond to the acidic and basic forms of the Co(II) reactant, probably. 

The net reaction rate does not behave as a simple second-order reaction or as a zeroth-order reaction. The net rate is linear to [Ca +][COf ], but not proportional to [Ca " ][C03 ]. At constant composition, temperature, and pressure, the net reaction rate is constant. The concentrations approach equilibrium and hence the net reaction rate approaches zero as reaction proceeds. 

Kinetic and equilibrium studies of the sorption of methanol on various coals and on partially acety-lated samples of these coals have been used to elucidate a mechanism for this process. The data are interpreted in terms of partial acetylation blocking surface sites and perhaps interfering with intermolecular hydrogen bonding. It is proposed that the rate-determining step is a set of parallel, competing, second-order reactions involving transfer of methanol from the surface to the interior of the coal. All types of surface sites appear to participate, and the pressure-independent rate constant is considered to be the sum of the rate constants for each type of surface site. The dependence of the experimental rate constant on methanol pressure is a characteristic of the coal rank. 

The variable k represents the rate constant. Note the order of each reactant is 1. The reaction order, which describes the order of the entire reaction, can be determined by adding the order of each reactant. For instance, in this example each reactant is first order (meaning each has an understood exponent of 1). The reaction order is the sum of the exponents, or 1 + 1=2. This is a second-order reaction. Most reactions have an order of 0, 1, or 2, but some have fractional orders or larger numbers (though these are quite rare). The order of the reaction must be determined experimentally. Unlike equilibrium expressions, the exponents have nothing to do with the coefficients in the balanced equations. 

Effect of H2S on Reaction Rate. As the desulfurization reaction proceeds, H2S is produced. This material, although mainly in the vapor phase, is in equilibrium with a concentration of dissolved H2S in the liquid. Under certain conditions the mass action effect of this material can strongly influence the overall rate of the desulfurization reaction. Figure 3 shows the effect for one set of circumstances of H2S partial pressure on the pseudo second-order reaction rate constant. Again the constant shown is not a true reaction rate constant— which would be independent of such parameters— but is an overall representation of several simultaneously occurring forward and reverse desulfurization reac-... 

If we assume that the second-order reaction given in equation 1 can be expressed as an equilibrium reaction, then K = kf/kr (K is the equilibrium constant, kf is the forward rate constant of the reaction, and kr is the reverse rate constant of the reaction.) If ° = -1.49 V, then K = 6.2 X 10 26. For the reverse reaction, which is spontaneous, we can assume an upper diffusion-controlled limit for kT of 1 X 1010 M"1 s"1 (17). Thus, k = 6.2 X 10"16, and we calculated a second-order half-life of about 200 billion years at 02 concentrations of 250 xM in the photic zone of the ocean. These rates and the... 

A kinetic rate model for aryl interchange was developed based on the following assumptions. The carbon-phosphorus bonds of the different triarylphosphines cleave with equal ease, and aryl interchange proceeds by a reversible second order reaction. For example, the reaction of a TPP and a TRI molecule always yields one MONO and one DI molecule, and there are nine distinct ways for the forward reaction to occur (any of the three aryls of one molecule can replace or be replaced by any of the three aryls on the other). Of the many possible ways for the molecules to react however, there are three which are unique. These and the respective chemical equilibrium constants are shown in Scheme 3. 

In this expression the speciation of S(IV) is separately calculated from equilibrium constants characterizing the solubility of S02 and the first and second dissociation of H2S03. Thus the three individual k values in Eq. 9 become second-order reaction rate constants that can be compared with those occurring in other systems (Erickson et al., 1977 Maahs, 1983 Hoigne et al., 1985 Hoffmann, 1986). Similar separations between the kinetic environmental factor, and the environmental factor controlling the speciations of P will be applied in Section 2. 

The rate is actually given by /[S20g ][I ] (a second-order reaction) and not k/[S20g ] [ 1 ], as might be expected from the balanced chemical reaction (a fourth-order reaction would be predicted). The only sound theoretical basis for the equilibrium constant comes from thermodynamic arguments. See Gibbs free energy in Section 6.3 for the thermodynamic computation of.equilibrium constant values. 

Note that 4T/h has units of s and that the exponential is dimensionless. Thus, the expression in (3.1.17) is dimensionally correct for a first-order rate constant. For a second-order reaction, the equilibrium corresponding to (3.1.11) would have the concentrations of two reactants in the denominator on the left side and the activity coefficient for each of those species divided by the standard-state concentration, C, in the numerator on the right. Thus, C no longer divides out altogether and is carried to the first power into the denominator of the final expression. Since it normally has a unit value (usually 1 M ), its presence has no effect numerically, but it does dimensionally. The overall result is to create a prefactor having a numeric value equal to 4T/h but having units of M s as required. This point is often omitted in applications of transition state theory to processes more complicated than unimolecular decay. See Section 2.1.5 and reference 5. 

Table 1 covers rate constant data on second order reactions, grouped by class, while Table 2 covers association reactions. Relevant equilibrium constant data are given in Table 3. AU concentrations are measured in molecules cm". Notes on each reaction, as well as related photochemical data, may be found in the reference.

The most important forms for reversible reactions are first order, forward and reverse, and second order, forward and reverse. If change in the number of mols occurs and order follows stiochiometry, the reversible reactions can also have forward and reverse steps of different order. Since in the following presentation we treat the reactions as elementary steps, the ratio of rate constants does define the equilibrium constant for the reaction, K = kf/k. ... 

In previous chapters, we have looked at a variety of reactions of coordination compounds. In Chapter 5, we found that the equilibrium constants for these reactions depend on the heat evolved and the amount of disorder produced (entropy). A favorable heat or entropy change is a necessary condition for the occurrence of a reaction. However, the reaction rate must also be sufficiently fast in order for a reaction to proceed. Reactions occur at a variety of speeds some are immeasurably slow, and others are complete in a fraction of a second. 

Reaction Second order reaction velocity constant, fc, (1 mol" s" ) Equilibrium constant, (moll )... 

When there is more than one substrate (see Multisubstrate enzymes), the kinetics may be second order (or pseudo-second-order. See Cleland s short notation). The equation for a second order reaction is A + B iib P, where kj is the bimolecular rate constant, and V = k2[A][B], All chemical reactions are reversible andd eventually reach an equilibrium in which the rates of the forward and reverse reactions are equal. 

The closeness of fit may be gauged from the experimental and theoretical rate vs. concentration curves for hydrolysis of p-nitrophenyl carboxylates catalysed by quaternary ammonium surfactant micelles (Figure 3). The shape of the curve is satisfactorily explained for unimolecular, bimolecular, and termolecular reactions. An alternative speculative model is effectively superseded by this work. Romsted s approach has been extended in a set of model calculations relating to salt and buffer effects on ion-binding, acid-dissociation equilibria, reactions of weakly basic nucleophiles, first-order reactions of ionic substrates in micelles, and second-order reactions of ionic nucleophiles with neutral substrates. In like manner the reaction between hydroxide ion and p-nitrophenyl acetate has been quantitatively analysed for unbuffered cetyltrimethylammonium bromide solutions. This permits the derivation of a mieellar rate constant km = 6-5 m s compared to the bulk rate constant of kaq =10.9m s . The equilibrium constant for ion-exchange at the surface of the micelle Xm(Br was estimated as 40 10. The... 

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